On diverging concertina tearing

A simplified theory of the process of concertina tearing of thin plates wit h two diverging cracks is developed. The cracks initiate from a local cut a nd propagate away from the initiation site as the loading punch is pushed i n the in-plane direction. At the same time the plate ship between the two c racks folds back and forth in much the same way as the ''concertina" collap se pattern of circular tubes, studied extensively in the literature. Closed -form solutions are derived for the punch force and the length of the foldi ng wave. Postulating a differential equation for the direction of the crack growth, a path of the tearing fracture is determined. It is shown that the crack trajectories depend on the plate thickness and the size of the initi ation cut but, perhaps surprisingly, are independent of the material proper ties of the plate. This means that the process of concertina tearing would be similar for metal, plastic, paper leather, etc. A series of experiments on 0.4-mm-thick mild steel plate was performed showing a very good agreemen t with the theoretical predictions.